What will come in place of (?) in the following number series?
138,210,66,282,-6,?

Options

A. 354
B. 320
C. 336
D. 348

Answer

To solve the number series problem: 138, 210, 66, 282, -6, ?, we need to identify the pattern in the series. Let's break it down step by step.

### Step 1: Identify the Pattern
First, we will look at the differences between the numbers in the series.

1. From 138 to 210:
\[ 210 - 138 = 72 \]

2. From 210 to 66:
\[ 66 - 210 = -144 \]

3. From 66 to 282:
\[ 282 - 66 = 216 \]

4. From 282 to -6:
\[ -6 - 282 = -288 \]

### Step 2: Write Down the Differences
Now we can summarize the differences:
- \( 72 \) (from 138 to 210)
- \( -144 \) (from 210 to 66)
- \( 216 \) (from 66 to 282)
- \( -288 \) (from 282 to -6)

### Step 3: Identify the Pattern in Differences
The differences appear to alternate between positive and negative:
- Positive: \( 72 \), \( 216 \)
- Negative: \( -144 \), \( -288 \)

### Step 4: Find the Next Difference
The positive differences seem to increase by \( 144 \):
- \( 72 \) to \( 216 \) is an increase of \( 144 \).

Following this pattern, the next positive difference should be:
\[ 216 + 144 = 360 \]

### Step 5: Calculate the Next Number
Now, we will add this difference to the last number in the series, which is -6:
\[ -6 + 360 = 354 \]

### Conclusion
Thus, the number that will come in place of (?) in the series is:
\[ \boxed{354} \]